This isn't much different from what I'm saying, I think -- you mention frequencies, which don't come up much in most study of music theory beyond more or less w

This isn't much different from what I'm saying, I think -- you mention frequencies, which don't come up much in most study of music theory beyond more or less what you have in your comment. Beyond that, well, I suppose you could say it's "math", but that's a bit like saying price comparing at the grocery store (calculate the per-kilo price!) is math -- it won't have math geeks drooling. I can recognize intervals by ear, but it's just practice. You start out by "cheating" (twinkle twinkle starts with a leap of a perfect fifth, the NBC call sign with a major sixth, etc.), then you just learn it. I'll bet you could get the gist of it using the reference melodies pretty quickly. You can refer to the relations using basic math terminology, or just the music theory technology, but regardless it doesn't feel like anything beyond elementary math -- it goes much quicker into psychology territory.